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Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2025 / Cilt: 29 Sayı: 3

Characterization of Tzitzeica Curves by Using q-frame in Euclidean 3-space

Gamze Nur Şen(ESKISEHIR OSMANGAZI UNIVERSITY)0000-0001-5687-4231
Gül Uğur Kaymanlı(CANKIRI KARATEKIN UNIVERSITY, FACULTY OF SCIENCE)0000-0003-4932-894X
Cumali Ekici(ESKISEHIR OSMANGAZI UNIVERSITY)0000-0002-3247-5727
Pages
688–693
Publication Date
2025-12-25
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Using q-frame in 3-dimensional Euclidean space, after defining T-curve and s-curve and investigating related theorems, the theorems related to sT-curves are proved.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, using q-frame Tzitzeica (T-curve), spherical (s-curve), and spherical Tzitzeica (sT-curve) curves are studied in three-dimensional Euclidean space.
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Key Findings & Data:There is a T-curve when its torsion has a non-zero constant ratio to the square of the distance from the origin to the plane generated by tangent and normal vectors at any point on the curve.
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Conclusion & Impact:Using q-frame in 3-dimensional Euclidean space, after defining T-curve and s-curve and investigating related theorems, the theorems related to sT-curves are proved.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Eğrilikler · Küresel eğriler · Tzitzeika eğrileri

Abstract

In this work, using q-frame Tzitzeica (T-curve), spherical (s-curve), and spherical Tzitzeica (sT-curve) curves are studied in three-dimensional Euclidean space. There is a T-curve when its torsion has a non-zero constant ratio to the square of the distance from the origin to the plane generated by tangent and normal vectors at any point on the curve. Using q-frame in 3-dimensional Euclidean space, after defining T-curve and s-curve and investigating related theorems, the theorems related to sT-curves are proved.

Özet

Bu çalışmada, q-çatısı kullanılarak 3 boyutlu Öklid uzayında Tzitzeica, küresel ve küresel Tzitzeica eğrileri analiz edilmiştir. Burulmasının, eğri üzerindeki herhangi bir noktada orijinden tanjant ve normal vektörler ile üretilen düzleme olan uzaklığın karesine oranı sıfırdan farklı sabit bir değere sahip olduğu bir Tzitzeica eğrisi vardır. 3-boyutlu Öklid uzayında Tzitzeica ve küresel eğrileri q-çatısı kullanılarak tanımlayıp ilgili teoremleri inceledikten sonra, küresel Tzitzeica eğrileriyle ilgili teoremler ispatlanmıştır.

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Cite This Article

Şen, G. N., Kaymanlı, G. U., Ekici, C. (2025). Characterization of Tzitzeica Curves by Using q-frame in Euclidean 3-space. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 29 Sayı: 3, 688–693. https://doi.org/10.19113/sdufenbed.1805264

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